Rangers boss Harry Redknapp, who signed Parker when he was manager of Spurs, confirmed on Friday that a deal had been done but that the move now hinges on whether Parker is prepared to drop down to the second tier.
Redknapp said: "We have made a good offer to Scott and we agreed terms with Tottenham, it's up to Scott now. We can't do any more, it's a good offer but it's up to him.
"If somebody else comes in he can go elsewhere, we haven't got an agreement with Scott yet, it's up to him what he does.
"We feel we are a club that are looking to get back up and if he comes and wants to be part of that he can.
"This is a club that is progressing and trying to move forward and we'd love him to be part of that."
The 32-year-old made 28 appearances last season for Spurs but does not appear to feature in Andre Villas-Boas' plans this term.